{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Levy Stable models of Stochastic Volatility\n",
    "\n",
    "This tutorial demonstrates inference using the Levy [Stable](http://docs.pyro.ai/en/stable/distributions.html#stable) distribution through a motivating example of a non-Gaussian stochastic volatilty model.\n",
    "\n",
    "Inference with stable distribution is tricky because the density `Stable.log_prob()` is not defined. In this tutorial we demonstrate two approaches to inference: (i) using the [poutine.reparam](http://docs.pyro.ai/en/latest/poutine.html#pyro.poutine.handlers.reparam) effect to transform models in to a tractable form, and (ii) using the likelihood-free loss [EnergyDistance](http://docs.pyro.ai/en/latest/inference_algos.html#pyro.infer.energy_distance.EnergyDistance) with SVI.\n",
    "\n",
    "\n",
    "#### Summary\n",
    "\n",
    "- [Stable.log_prob()](http://docs.pyro.ai/en/stable/distributions.html#stable) is undefined.\n",
    "- Stable inference requires either reparameterization or a likelihood-free loss.\n",
    "- Reparameterization:\n",
    "    - The [poutine.reparam()](http://docs.pyro.ai/en/latest/poutine.html#pyro.poutine.handlers.reparam) handler can transform models using various [strategies](http://docs.pyro.ai/en/latest/infer.reparam.html).\n",
    "    - The [StableReparam](http://docs.pyro.ai/en/latest/infer.reparam.html#pyro.infer.reparam.stable.StableReparam) strategy can be used for Stable distributions in SVI or HMC.\n",
    "    - The [LatentStableReparam](http://docs.pyro.ai/en/latest/infer.reparam.html#pyro.infer.reparam.stable.LatentStableReparam) strategy is a little cheaper, but cannot be used for likelihoods.\n",
    "    - The [DiscreteCosineReparam](http://docs.pyro.ai/en/latest/infer.reparam.html#pyro.infer.reparam.discrete_cosine.DiscreteCosine) strategy improves geometry in batched latent time series models.\n",
    "- Likelihood-free loss with SVI:\n",
    "    - The [EnergyDistance](http://docs.pyro.ai/en/latest/inference_algos.html#pyro.infer.energy_distance.EnergyDistance) loss allows stable distributions in the guide and in model likelihoods.\n",
    "\n",
    "#### Table of contents\n",
    "\n",
    "- [Daily S&P data](#data)\n",
    "- [Fitting a single distribution to log returns](#fitting) using `EnergyDistance`\n",
    "- [Modeling stochastic volatility](#modeling) using `poutine.reparam`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Daily S&P 500 data <a class=\"anchor\" id=\"data\"></a>\n",
    "\n",
    "The following daily closing prices for the S&P 500 were loaded from [Yahoo finance](https://finance.yahoo.com/quote/%5EGSPC/history/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import os\n",
    "import torch\n",
    "import pyro\n",
    "import pyro.distributions as dist\n",
    "from matplotlib import pyplot\n",
    "from torch.distributions import constraints\n",
    "\n",
    "from pyro import poutine\n",
    "from pyro.contrib.examples.finance import load_snp500\n",
    "from pyro.infer import EnergyDistance, Predictive, SVI, Trace_ELBO\n",
    "from pyro.infer.autoguide import AutoDiagonalNormal\n",
    "from pyro.infer.reparam import DiscreteCosineReparam, StableReparam\n",
    "from pyro.optim import ClippedAdam\n",
    "from pyro.ops.tensor_utils import convolve\n",
    "\n",
    "%matplotlib inline\n",
    "assert pyro.__version__.startswith('1.7.0')\n",
    "smoke_test = ('CI' in os.environ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([23116])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = load_snp500()\n",
    "dates = df.Date.to_numpy()\n",
    "x = torch.tensor(df[\"Close\"]).float()\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(9, 3))\n",
    "pyplot.plot(x)\n",
    "pyplot.yscale('log')\n",
    "pyplot.ylabel(\"index\")\n",
    "pyplot.xlabel(\"trading day\")\n",
    "pyplot.title(\"S&P 500 from {} to {}\".format(dates[0], dates[-1]));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of interest are the log returns, i.e. the log ratio of price on two subsequent days."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(9, 3))\n",
    "r = (x[1:] / x[:-1]).log()\n",
    "pyplot.plot(r, \"k\", lw=0.1)\n",
    "pyplot.title(\"daily log returns\")\n",
    "pyplot.xlabel(\"trading day\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(9, 3))\n",
    "pyplot.hist(r.numpy(), bins=200)\n",
    "pyplot.yscale('log')\n",
    "pyplot.ylabel(\"count\")\n",
    "pyplot.xlabel(\"daily log returns\")\n",
    "pyplot.title(\"Empirical distribution.  mean={:0.3g}, std={:0.3g}\".format(r.mean(), r.std()));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting a single distribution to log returns  <a class=\"anchor\" id=\"fitting\"></a>\n",
    "\n",
    "Log returns appear to be heavy-tailed. First let's fit a single distribution to the returns. To fit the distribution, we'll use a likelihood free statistical inference algorithm [EnergyDistance](http://docs.pyro.ai/en/latest/inference_algos.html#pyro.infer.energy_distance.EnergyDistance), which matches fractional moments of observed data and can handle data with heavy tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model():\n",
    "    stability = pyro.param(\"stability\", torch.tensor(1.9),\n",
    "                           constraint=constraints.interval(0, 2))\n",
    "    skew = 0.\n",
    "    scale = pyro.param(\"scale\", torch.tensor(0.1), constraint=constraints.positive)\n",
    "    loc = pyro.param(\"loc\", torch.tensor(0.))\n",
    "    with pyro.plate(\"data\", len(r)):\n",
    "        return pyro.sample(\"r\", dist.Stable(stability, skew, scale, loc), obs=r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 0 loss = 8.961664199829102\n",
      "step 20 loss = 4.8506011962890625\n",
      "step 40 loss = 1.5543489456176758\n",
      "step 60 loss = 1.7787070274353027\n",
      "step 80 loss = 1.4140945672988892\n",
      "step 100 loss = 1.3671720027923584\n",
      "step 120 loss = 1.287503719329834\n",
      "step 140 loss = 1.2791334390640259\n",
      "step 160 loss = 1.2810490131378174\n",
      "step 180 loss = 1.2784368991851807\n",
      "step 200 loss = 1.2823134660720825\n",
      "--------------------\n",
      "loc = 0.0003696\n",
      "scale = 0.00872\n",
      "stability = 1.977\n",
      "CPU times: user 15.6 s, sys: 521 ms, total: 16.1 s\n",
      "Wall time: 2.38 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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IiIgyBIODGWBiWVG8kiIgGByc7htDICBHfU7fqBv+gAyjQdK2MIcqybUAUDIHoVOSEjnaOYI9zUMwGSRkW4zw+AM42Zt4IRsRERERTT0GBzOAyBz0acFB9ElFwrzibJiNEpwePzrVXQYTiR0HFXlWGEP2JAgic+DxB2B3+SK+H4vIGly/aq62L4GlRURERESZgcHBDFAW0nMgy7K2eyBWcGAyGrRehFilRfH6DQBlSlKuVZmSNKCztGjI4cEzB5QG5H/cNA+rqpSJR4cZHBARERFlBAYHM4Ao++keceGbzzbi7VPKeNDV6rjRaBL1HYgxpnMLIycVCaVqaVG/zqbkP+xpg9sXwMqqfJxfW4QVVWIcKhepEREREWUCBgczQHm+kjloHnDiUbVs59+3LMPKqjjBQVmw7yAakTmojJE5AIASbWKRvszBi0e7AQD/sGEeJEnSMgfHuuwJtzUTERER0dRjcDADiJ4DALCYDHjg9vNw56V1cV9TJ5qSex1Rvx9vx4EQzBzoCw5EH0N9ZT4Apfchz2qC2xfAyQRjVYmIiIho6jE4mAFyrSasqMxHSY4Fv/vEBtywujLha+aoE45iXdiLRuVoY0yFEm2caeKyIn9A1hqmxWcbDJIWKLDvgIiIiCj9TOk+AJ09SZLw9NbNCMgyrKbIvQbRaKNIHdEv7LuGRUNyvMyB/l0H/WNuBGTAaJC0oAIAVlUVYFfTII52jADranSdnYiIiIimBoODGcJsTC4JVJyjXKCPjHvh9QfCXu/zB7Rty/F6DkpDdh0kIsqUynLDR6OuqubEIiIiIqJMwbKiWaowywxxjT7kDL+47x1V7vKbjZKWHYgmmcxBj7ptuWJCsLGiUgkOGtmUTERERJR2kwoOfvWrX+G5557T/vylL30JhYWF2LRpE1paWlJ2OJo6BoOEomzlzv/ghNIibQFavg2GKAvQhJKc+KVJobTgIC882FhYmoMcixEub0Db7ExERERE6TGp4OA73/kOsrKUWvR33nkHDQ0N+N73vofS0lLcfffdKT0gTZ1i9eJ+cEJZUOewmFQUu6QIAErVC/3+UT2ZA7UZecJ7GgySlj3gpmQiIiKi9JpUcNDW1oZFixYBAJ5++mnccsstuPPOO3Hfffdh27ZtKT0gTZ3iGHf+ReYg3hhTAChV+xZG3T64vP64z+0WmYP8yIBjRRUnFhERERFlgkkFB7m5uRgYULbwvvTSS7j66qsBADabDePj46k7HU0pMbEosqxIzRzEGWMKAPlZJpiNStlRotKinjjBgdjW3D7k1HFqIiIiIpoqk5pWdPXVV+MTn/gEzjvvPJw4cQJbtmwBABw9ehTz589P5floCsXMHAyLSUXxMweSJKEkx4puuwsDY25UFcZ+vggO5kQJDkRjc5+OqUdERERENHUmlTloaGjAxo0b0dfXhyeffBIlJSUAgH379uEjH/lISg84FRoaGlBfX4/169en+yhpJcaZDjrCewZEWdHE/oBoSvP0bUkWo0wr8iOnH4ngYEDnpmUiIiIimhqTyhwUFhbigQceiHj8m9/85lkf6FzYunUrtm7dCrvdjoKCgnQfJ23EtKGJZUWdI/oyB0DoONPYd/3HPX7YXT4AkaNMAWX3gfIebsiyDEmKPSGJiIiIiKbOpDIHL7zwArZv3679uaGhAWvXrsXtt9+OoaGhlB2OppZWVhRyYe/xBbQsQKKeAwAoyUm860CUFGWZjcizRsajovfB5Q3A4Ynf2ExEREREU2dSwcEXv/hF2O12AMDhw4fx+c9/Hlu2bEFTUxPuueeelB6Qpk60zEH3iAuyDFhMBu378YiyonhbksWkojkFtqhZgRyrCVlmo/o+LC0iIiIiSpdJlRU1NTWhvr4eAPDkk0/ihhtuwHe+8x3s379fa06mzFccZVpRx7DSb1BVmKWrvKc0icxBtH4D7X3yLGgbHEf/mBvzSnISH56IiIiIUm5SmQOLxQKnUxk7+corr+Caa64BABQXF2sZBcp8oqxoyOmBPyADADrV4KBSR0kRoC9zEG+MqSDKk/pGObGIiIiIKF0mlTm4+OKLcc8992Dz5s3YvXs3Hn/8cQDAiRMnUF1dndID0tQpylYu7AMyMOz0oCTXGgwOdDQjA/p6DrpH1O3IcYIDbWKRg2VFREREROkyqczBAw88AJPJhCeeeAIPPfQQqqqqAADPP/88rrvuupQekKaO2WhAQZYZQLC0qHNEZA70BQd6phX1jCbOHJSJkajMHBARERGlzaQyB7W1tfjrX/8a8fiPf/zjsz4QnVslORaMjHsx4PBgMYAOdQFavIVmoUq1vgU3/AEZRkNkn0LPiP6yokT7EoiIiIho6kwqOAAAv9+Pp59+GseOHQMArFixAjfddBOMRmPKDkdTrzjHgjP9jmDmYDi5zIHoWwgtTZooOK0oTkNyrtjWzOCAiIiIKF0mFRycOnUKW7ZsQUdHB5YuXQoAuO+++1BTU4PnnnsOdXV1KT0kTR1t14HDA1mW0ZVkQ7LJaEBRthlDTi/6xyKDA1mW0WtXLvjL8+L0HOSpmQOWFRERERGlzaR6Du666y7U1dWhra0N+/fvx/79+9Ha2ooFCxbgrrvuSvUZaQqJBWSDYx7Yx33aEjK9mQMgpJk4SknQkNMLjz8AgGVFRERERJluUpmDN998Ezt37kRxcbH2WElJCb773e9i8+bNKTscTb3inGDPgNhxUJJjgc2svzysJNeCk71AX5QLezHGtCTHAospdiyqNSTrDA7sLi9OdI/ivNqiqH0ORERERJS8SQUHVqsVo6OjEY+PjY3BYkm8VZcyR3GOGCHqSbrfQAhmDiJLgkS/QXmcrEHoe9hdPrh9flhN8YOTLz9xCM8f6cbC0hx8+rI6fHBtVdzgg4iIiIgSm9TV1A033IA777wTu3btgizLkGUZO3fuxKc//WncdNNNqT4jTaGSnOCW5OAYU339BkJwnGmUzIE6qWhOnO3IAJBvM8OkZgDiLVQTGruUZXtn+h340hOHcNn3X8fRzpGkzi10j7jw9LsdCKiL4IiIiIhmq0kFB/fffz/q6uqwceNG2Gw22Gw2bNq0CYsWLcJPfvKTVJ+RplBxSHDQMenMQewtyT1qM3K8fgMAMBgkrf8hUXAQCMhaluPT76tDaa4VnSMu/Hl/R1LnBpSG6X/+1R782+MH8MLR7qRfT0RERDSTTKqsqLCwEM888wxOnTqljTJdvnw5Fi1alNLD0dQLnVbUmeSOA6EkTuZAlBUlCg4AJQPRY3cn7DvoHXXD61d2KnzhmiWoLLTha88cRcugM6lzA8CbJ/pwtFPJQuxtHsKWVXOTfg8iIiKimUJ3cHDPPffE/f7rr7+uff2jH/1o8ieic0rcrR9yeNAxpFxcT7bnIGpZkbbjIHFwIIKMaI3NodrVc87Jt8FkNKC2OBsA0DLg0H9o1YNvnNa+PtIxubIkIiIioplCd3Dw7rvv6nqeJHFyzHQiMge+gIwTPWMAkg8OtNIkZ7SyIpE5iN9zAMQvTwolyp+qi5Rzzi/JAQC0DDgRCMgw6JxetK9lELubBrU/H+0cSer1RERERDON7uAgNDNAM4fVZESu1YQxtw9jbh+A5BuStabmqD0H+suKyuJkIEK1DynBQZUaHFQVZcFokOD2BdA76taVpQCAh9Sswa0XVOO5Q11wePw40+/AovJcXa8nIiIimmk4+5G0O/8AYDEaUJqT+C5/qCL19Q6PHy6vX3vcH5Ax4FAChrK8xO8pSpz0BgfVRUo5kdlo0LIIzTpLi453j+KVY72QJOAzl9WhvjIfAHC4Y1jX64mIiIhmIgYHFBYczC20JV1Wk28zwWxUXjMUUlo05PRAVqeDFmcn3n8Rb19CKNFzUB1S/pRs38H/vKlkDa5fOQd1ZblYVVUAADjcbtf1eiIiIqKZiMEBaWVBAFBZkFy/AaD0mRRlR/YLiK+Lss0wGRP/qsVrbA41secACO870OO1470AgH/avAAAsFINDtiUTERERLMZgwMKyxwk24w88T1CMwcD6kW+mEKUiJ6yIlmW0TGhrAgA5pWIzEHi4MDl9WPY6QUALC7PAwAtcyCakomIiIhmIwYHhOLcYHBQlWQzsvYeIcvUhH7169DMRDyiIXnQ4YE/xgV6/5gHbl8AkhQ+HlVkDvT0HPSNKsGHxWRAfpbSk19XloMss1FrSiYiIiKajRgcUHhZ0SQzB6IpObysSLkIL9WZORABRkAOz0CECt1xYDEFf31F5qB1wAlZjn/nv3dUmaBUnmfVRu+ajAatKZmlRURERDRbMTggFIdMJ5pscFAStaxIzRzk6sscmIwGFGWbAcQuLRL9BhO3ONcUZ0OSgFG3Lyx7EU2vXXnvieNVtaZkBgdEREQ0S83K4KChoQH19fVYv359uo+SEVKRORB3/QdCLswHtLIi/aNRE00sCo4xDT+nzWzEXPVivzlB30GvWlZUPmG86koGB0RERDTLzcrgYOvWrWhsbMSePXvSfZSMEN6QfJY9B1HKivRmDoDEE4tEWVFVUWQQUytKiwbj9wyIxWwTgwOtKbmDTclEREQ0O83K4IDCzSvJhtVkwMKyHGRbdC/NDqMFB87IzEFpEsGBCCRE0/BE0SYVCVpTcr/OzMGEsqK6shzYzAY2JRMREdGsNbkrQZpRCrMteOnuS5FjnfyvQ7RpRcmOMgVCyopi9A3EKisCgHnaroP4F/axyopMRgPq5+Zjf+swjnSMYFF5ru5zExEREc0EzBwQAOXCWu9UoWiiBwfJjTIFglmG/iiZA1mWYzYkA8B8tawoYc+BKCvKjyyhWlGplBa91z2q+8xEREREMwUzB5QSIjgYdio7Crz+AEbdPgCTyxxE6zkYcnrh9PgBRG+cDvYc6CsrqsiPPNdctedCBBBEREREswkzB5QSRdnBHQUj414tg2A2Ssi36Y9Bg8FBZFmR6Dcoy7PCZjZGfF+UFQ06PBgZ90Z9f48voJ2tPC8ycyAe64uzpZmIiIhopmJwQClhNhq0IGDQ4dZKiopzLNqiMT1EQ3K0XQViUlG0fgMAyLWatOCiNUZpkbjoNxslbadCKNGHIHYhEBEREc0mDA4oZUT50KDDi36H2oycxI6D0OcPONwRm47j9RsIou+gJcY4U63fIM8WNWgpV0uNxBZlIiIiotmEwQGljLgTH5o5SGbHAQAUq893eQNaf4HQHmeMqSD6DlpiZA5Ev0FZXvSgRZQVDTm98PgCSZyciIiIaPpjcEApU5wTHEMqxpgmOwEpx2KExaT8Wk4sLYo3xlQI7jpIlDmIfq6ibDPMRiWjwL4DIiIimm0YHFDKiJGlQw6PtqcgmTGmACBJEkrV10zcdRBvO7Igphj1xFiiFpxUFH0TtCRJKFMDmliL2IiIiIhmKgYHlDJFIRf1/ZNYgCYUa03J4RfnnWrPQXWcngNRxjQQ466/aDSOlTkAgiVHHGdKREREsw2DA0qZkpBFaKIkKNmeAyBYnhQ6ztTl9cPuUvYmRFteJpSK0qYoo1ABoGdULECLFxyouw6YOSAiIqJZhkvQKGVCtyQPO5U9A6WTCA5KomxbFnf8rSZD3L0JWuZAnXY0cSKRljmIE2AEJxYxOCAiIqLZhZkDSpnQ4ECU9SQ7ylR5TWRw0DcWvOMfb2+COIPXL2uZhlDigj9eWZH4Xh/HmRIREdEsw+CAUiY0OOg/m7IirW8gMnMQbatxKJvZiFyrSX19+J1/nz+AAUfi9xHf4yI0IiIimm0YHFDKiOCgx+7SdgScTeZgIKQhWc8df+31udGnHfWPeSDLgNEgxZ2ipGUOOMqUiIiIZhkGB5QyIjgIqIuNcyxGZFmMSb+PCCjCeg5G4+8nCH999IlF4j3Kcq0wGGKXJmk9B8wcEBER0SzD4IBSJttihNUU/JUqnkRJUejropYVxWkkFsT41ImZgx7tPeIHGGKUaf+YGwER6RARERHNAgwOKGUkSdKyB8DkSoqU10WZVqSWFZXp2JtQGiW4UN5DZB/iBxiluVZIEuALyBh0Rh+JSkRERDQTMTiglAoNDiYzxjT0Pca9fjg9ysQhLThIcNcfCAYlEWVFOjMHZqMBxdmWsNcQERERzQYMDiilUpE5yLWaYFFYYROMAAAgAElEQVTLk8Td/75keg7UoKTfEStzkPg9tC3JHGdKREREswiDA0qpsOBgkpkDSZLCSouUEaTKhX6ikiDlc+NnDip09C2I3oY+HYvQ7C4vOofHEz6PYpNlGX2jbhzpGNEmXREREdG5xw3JlFLhwcHkMgfifbpGXMrOBJ0jSIXSnFg9B/rHoZbn6duSHAjI+Mj/7sTJ3jG88YXLUFmYlfC9Kehw+wi++8IxHOsa1XpMPnNZHb583bI0n4yIiGh2YuaAUqokBT0HQDDI6B9za6U9pbmWuCNItTPEnFakryFZeY7Ykhw/OHjtvV4c7bTD4wvgUPtwwvelcA9vP4O3Tw2ENZ9vP9mfxhMRERHNbgwOKKWKUtBzACgTgwClrEjvdmTtc9WgZMiplCQBgD8go39MlBWlrufg4e1ntK+bB5y6zkdBLeq/2ddvrMdLd18KADjePTqp0qJAQMaxLjvHzxIREZ0FBgeUUiUp6DkAgpmDQYdH21SspxwIAIqyLZAkQJaBIacXgJI1CMiAyRA+bjUWEYjEm1Z0pGMEO88Man9u7nfoOt9M0jvqwjefPYpXj/VAlpO/KG8fUoKD9fOLsbg8F/k2Ezz+AE70jCb9Xv/vhfdw/U+34Yn97Um/NhW8/gBGXd60fDYREVGqMDiglCoOyRakIjgYCM0c6LjjDyi9CUXZ4vXKa8/0KRfutSXZMBkT/9qLz+obix0c/GJ7EwCgIMsMAGgemH3BwR92t+GXbzfjn3+1F3/30A7sOK2/JMjp8aFf7QupKc6GJElYWVUAQAm8kjHk8OBX7zQDALaloSxpYMyN99+/DRd951X02jnhioiIpi8GB5RSxTnm4NfZkw8OSrSm4mDPQZnOsqLw1ysXn2f6xwAAC0tzdb1ea0i2u6PeEe8eceHZg50AgM9fswQA0Nw/+8qKTveNaV+/2zqM23++C/c9f0zXa9uHlAlP+TaTFmCtEsFBZ3LBwW92tsDlVUqRjib52rNld3nxsUd240TPGBwef1qCEyIiolRhcEApNa8kB2tqCnHD6rm67tDHUhLac5DElKHg64MNzQBwule5iK0rz9H1elFWNO71Y8zti/j+r95phi8g48IFxbhxdSUAoNvuwrjHr/uMM0GTWkr1Xx9ciQ9dUA0AeP5wt67Xtqr9BjXF2dpjK9Tg4HCHXfcZXF4/frWjOexMjig/s6kw7vHjE4/uxdHO4Hn3tgydk88mIiKaCgwOKKXMRgOe2boZD9x+/lm9T1hZ0aSCA7HrQGQOlIvYOp2ZgyyLEXlWZdLvxHGmXn8Av9/VCgD45CULUZRj0e58twzOntIiWZbRpJZrbVhQjC9etxSA0kfg9iUOktrUfoOaomBwIDIHx7rs8Pr1NSX/+d0ODDg8qCrMQlmeFbIMvNetP7g4G5/7w7vY3TyIPKsJn7tyMQBgb/NgglcRERFlLgYHlJFCl6D1iRGkOpaXCaUhrweCPQcLy/RlDgCgLD9YWhSqbdCJkXEvssxGXLmsHAAwv1R539nUlDzg8GDU7YMkAbXF2SjLtSLXakJADmYF4mkbVMqKaoqDuyHmFWcj12qCxxfAqd6xWC/VBAIyfr5NmRj18c3zsbIyHwBwJInMw2T12F14qbEHBgl45OPr8bGN8wAAJ3vHMOz0JHg1ERFRZmJwQBlJlAU5PX50a/sJJpE5cLgx7vGjQ91gvLBMX+YAAMpyo48zbRlULnznlWRrexfmlyh3v5tmUd+BKCmqKsyCzWyEJEla8HVGR5CkZQ5CyooMBgkrtAv8xL0Dr77XizN9DuTZTPjwhbVaQ/O56DsQY1iri7Kxfn4xSnKt2t9/H0uLiIhommJwQBkp12qCRe1ZEGPrS5PYuBzsOfBozchF2WZdY0wFkamYuAitRb3wnVcSvKidX6JcFLbMoolFoqRoQWkwGyO+FpmaeNoGI8uKACQ1sej3u1oAAB/dMA+5VpMWWIT2AEwV8bOuDQlu1s8rBgDsaWZwQERE0xODA8pIkhS+j6Ao2wyLSf+vq1jANjDmDikp0p81AGJvSRaZAxEQAMD8UpE5mD3BgcgOhAYHYhpUU3/8kiBZlrVpRaFlRUDoxKLEF/in1GlJVy5XyrtWVCqvPdEzuUVqyRDBTW1IkLhufhEAYF8L+w6IiGh6YnBAGSs0ONC7HVkozQ02NGvBQan+fgPlM0VZ0YTgYCDyojCYOZg9ZUXNUYKDBWpZTaIgadjp1aZAVUdkDpS7/42ddvjjbDv2+QPoHFZKvkT2obooC/k2E7x+eVKL1JIhgsTQzMG6+Urm4GD7iK6mbCIiokzD4IAyVugSNb0L0IKvDU4rErP468qTyxxUFSl3tCcuNxN/Ds0ciAvk2TTOtClq5kBfWZHoNyjPs8JmNoZ9b0FpLrItRox7/TjTFzsD0W13wR+QYTZKWiAnSZKWPWic4tKiVtF7UhwaJGajNNcCjy+Q9CI3IiKiTMDggDJWSUjmoCyJZmQgmHUYc/twrEu5SEw2c7BsTh4A4Hj3KALqHWx/QEa7OmUntOegMNsyqzYlBwIymgZERiYYdIlAYcDhwYjTG/P1wUlF2RHfMxok1M9VsgeH41xgi7KkqsIsrTEcQEjfwdRenEfb0yBJEtax74CIiKaxWRkcNDQ0oL6+HuvXr0/3USiO4pxgQJBsWVG+zQSzUblgPKmOxEy252B+SQ6sJgOcHr92l7hrZBwefwBmo4S5BeG18mKc6WxoSu4cGYfHp/w7VBYGfzY5VhMq1CzPmTh9B61aM3JW1O8Hm5Jj3/3XGpqLYzQ0T2HmYMztw4A6Jje0vAwI9h1w3wEREU1HszI42Lp1KxobG7Fnz550H4XiCCsrSjJzIEmS1pQMACaDFHanXw+T0YAlFUr2QCzVCr1bbAy5Ww0AC2bRONPm/mC9/cRN2MGm5NhBUrQxpqGCF/iJMwfVEwIMkTk41hW/Z+FsiN+Domwz8m3msO+JvoN9LUNaxomIiGi6mJXBAU0PoWVFyfYcAOHBRW1xNszG5H/dRWnRsS6lubV5IHJSkTCvZPYsQhPTiBZE2TgtmpLj9R3EGmMqiH0BHWoAEE0wOAh/j4VlubCZlYzPVJV4tWqTiiJ/D1ZU5sNmNmDI6Y2bPSEiIspEDA4oY53NtCIg2JQMJLcZOdTyucG70ED02faCqLefDT0HYoxptH9X0dsRL3OgXdgXRy8rqlB3TPSOuiDL0e++i+zDxMyB0SBpPze9+w5kWcZvdrbg07/Zp2u7cetg7N8Ds9GA1dWFAIADbWxKJiKi6YXBAWWssykrAoDSkOAi2X4DYdlcUVakZA5atMxB5EWhKFuaDcGBuPCPlkFJtCU5EJC1jECszIHYTu31yxiK0djcESNzAIQ0JeuYGOT0+HDXHw7gP58+gheOduPZg50JXxNtUlGoBSWJMx9ERESZiMEBZazQnoGzLSuqm2TmYNkc5SKzddCJUZdXu/CfF+WiWGQOeuxuOD2+SX1eOgUCMr7910b85p3mhM+NNsZUWBCyCC1azX3PqAsefwAmg4S5BdEzQhaTQSsr67G7Ir7v9QfQNSICjMjsg/i5iWb0WJr7Hbi5YUdYQHCwPXFAoe26iBEciDG4ncMMDoiIaHphcEAZq6ooC0sr8rB5UQmyLaakXx9eVjS5zEFxjkWbvnO8ezR4xzhK5qAw24LCbKU5daqXobUPOXGkYwSNnXac6BmF13/224D3NA/i4e1N+OazjbC7Yo8h9fgCWllQtLKimqIsmAwSXN4AuqNc2IsxppWFWRHNzKHK1dKiaMFB17ALARmwmgxRx9yKRudEd+4/87v9ON4zirI8K/7lsjoAwMG24bivAUJ7DqIHB5WFSnDQweCAiIimmeSvuIjOEbPRgOc/dwkkKfFzowltaE52x0Go5XPz0WPvw7aT/XB6/DBI0UtZACWjMOwcRnO/Q6t7T7VdZwZw2//uDHvswgXF+OOnNp7V++5uUkZv+gIydpwawHUr50R9XtuQE/6AjGyLMWq5l8loQG1JNs70OXCmz6FdKGuv10aQRu83ECryrTjWBfTa3RHfa1f7DaqKsiBF+QWpCrk4l2U56nOcnuAOjKc+swk2sxEPvnEap/rGMOb2Idca/X8eff6AFnTEyhyI8a7MHBAR0XTDzAFlNINBinphp0epmjkozDaHNTcnS5SovHi0G4ByV9hiiv5fncXqFuZjao/CVPjj3nYAQJ7VhFK1dGpfy9BZZw92NQXn8r95oi/m85r6gv0GsX42C0NKiyZqTTCpSKjIi505iDWpSBBNymNuH+zj0Uu8RGlUcY4FNcXZKMuzoqowC7IMHI5TWtQ14oIvIMNiNGBOfvSyqOpCNXOhBidERETTBYMDmrFWVxegIt+Km9ZUTjrAAIDlE5qSozXhCivVRtjGKdrO6/b58VKjEqT84h/XY/e/XwWLyQB/QEbXcORFtF5efwD7WoIbfd883hvzolbrN4jTxxGvKTnRjgNBlHP1jEYpTRqKv0TNZjZqgZN47kRi1Gpo38TqamW/wqH22KVFIripLg7fzBx29gIrJAlw+wIYdCSefkRERJQpGBzQjFWSa8XOe6/Etz6w8qzeZ2J5ULxlait0bPY9G9tO9GPU5UN5nhXr5hXBYJC0C2Rx0ToZh9pHMO71oyDLDIvJgM4RF07FaOZtUpuy45VqiQvuaLsOYi0vmyjYcxCtrCh+5gAILy2KRgQ5C8OCA2UE6cE4wYHoJ4k1qQgArCajNnGJfQdERDSdMDigGe1sMgbCgtIcWEIaZ+MFB8vn5kOSgG67C/1jkRe1Z+u5w10AgC2r5mp3rUXd+9kEB7uaBgAAFy0sxoYFyobfWKVFLXEmNgnxdh3EG0EaStt1ELWsKPqOg1Di/WM1JZ/pU4Kf0Gb1NTVKcHcwzn4CrRk5QeaDE4uIiGg6YnBAlIDZaMCi8uAFZLyL4lyrSbtrrncBl14urx8vN/YAAG5cM1d7XFykxiqf0UM0I1+4oATvW1IGIHZw0Nwfe2KTIP4N2oecYb0QiUaQhtLKiqJkDsTEo3ilSeLivD1GcBBtHOuqqgJIknK3P1Zwpy1Ai/N7AIROLJp8uRcREdG5xuCASAexDA2I33MAACsrRWlRavsO3jzRhzG3D3MLbDivpkh7vOYsMwc+fwB7m5V+gw0LinHZ0nIAwK4zgxH7Gjy+4MV9vLKasjwrrCYDAnL4nfPuEWUEqcVo0BrGYxHNvn1jbvhD9iW4fX6tDyFe5iBYVhT57yLLslbyFLoDI89mRp2aSYjVd6A7cyA+X+citD3Ng9jXMpj4iURERFOIwQGRDvUhfQeJLgq17bwTmpL3tQxhNM7+gESeO6SUFL0/pKQICAYHbZMMDhq77Bhz+5BnM2H53HzUleWgqjALHn8Au86EX6y2DzkRkIEsszHqfgFBkiTtwl3c5QeC9feVhbaYzbxCSa4VBgnwB2QMOIJ38buGXZDVM5TEmUIlPj9azX//mAejbh8MUuSuAtGUfCBKaZEsy8GegziZEyAYHOgpK3pkexM+9LN38JGf78Kwkw3MRESUPgwOiHQQTclz8m3IshjjPnel2pQcWlb03KEu3PLQDtzzx4OT+nyX149XjiklRe9fPTfse7VnGRyIAODC+cUwqqNj37c0emlRS8gSuET9HDVRyp309hsAgNEgaQFI6K6DtpB+g3hniFdWJPoNqouyYTWF/zzX1ihNydEyByPjXoy6lGxKolGsoqyocyR2cCDLMr7/4nv41l8bASiZmXdOD8R937Px3KEuXP/TbfjGX47iQNswx6wSEVEEBgdEOly0sASfvGQBvnFTfcLnisxBy4ATI+NKpuD3u1sAAK8c65nURfzr7/XC6fGjqjBLu3gVxEX4kNMbd7NxLKIZecPCYu2xWH0HrQP6SmqA4MVz6N9XXKhXFcbvNxAqomxJ1jvtSHzGsNMLhzu8POpMlH4DQZtYFOXiWWQNyvKsCYPERIvQZFnGfzx9BA2vnw47y7ZT/XHf92w8+MYpHOuy49Edzfhgw9u48odvYn/rUOIXEhHRrMHggEgHo0HCf7y/HtetnJvwuYXZFu3CtbHTjs7hcexQ7wbLMvDY7takP/+VY70AgC2r5kTcLc+1mrTymmQDj0BA1pqRNywo0R7fVFcCo0FCU78j7OJWb0kNENyA3DYUWlYU3GysR3le5DjT4KSi+GfIs5lRkGVWPzf8Al0bYxplV8PyuXkwGyUMOb0RWQcx3rUuzo4HQSxC6x/zwOX1R3z/QNswfr+rFQYJ+M7Nq/DV9y8HAGw/OTXBwZDDg0Z1I/SWVXNgMxtwpt+BB18/NSWfR0RE0xODA6IpENp38Od3OyDLQJ7NBEDZcDxxm/Ggw4O9zYP44942PK+OKxVkWca2k8odfNEsPNFk+w7e6x6F3eVDjsWonRlQLqzFtufQxmq9k3qA6JkDcZGe6K6/EJxYFMwcBCcVJX4PkT1onzDJSRtjGiVzYDUZtTKyA23hpUUn1eBgcXlexOsmys8yIUfNLkTLHoilc1csq8DtG2qxYWEJTAYJrYNOLUOTSruaBiDLyhbvBz96AZ78zCYAwPZT/Rj3RAYvREQ0OzE4IJoCoROLntzfDgC49/rlKMuzon/MrY0kHXF6cetDO3D+f72MW3/2Dr70xCF85nf7w+rOj/eMonfUDZvZgAvmFUV+GEKDg+Rm6u9Vp+OcP68IJmP4/xysqIzsndCzAGzimUIvzFNTVqQvcwAEMxQTJwad0TIHuRGvAYJNyYcnTJw61atsyV5cEf11oSRJCvYdRBlnerBdee/zapUyplyrSft6+xSUFons1aY6JUNUPzcfVYVZcHkDeHsKS5mIiGh6YXBANAVEU/JLjT040+eAzWzAjWvm4rZ1NQCA3+9qhcvrxyd+vQd71TvIlQU27aL5mQMd2nttO6FcuF20sAQ2c/Q699riyW1JFnev180rjvjeyqrwqUuBgBzWkJyIyBz0j3ng9PgQCMjoUi+S9ZYVTcwcyLKM1kH92QfxnPaQO/def0C7Mx+t5wAIBncTJ06JzEHo3ot4tOAkyjjVg2pWYk11sIfk4kVKr8f2U9F3TITyB2T8YXer7iyDFhwsKgWgBC9XLVcyUa++16PrPYiIaOZjcEA0BVaoF9ZOtVzjuhVzkGcz48MX1kCSlDvDdzyyG3uah5BnM+H5z12CHfdeie9/aDUA4Pkj3fD4lNKjt9SSoksWl8X8vGhbkh/b3Yrb/ucdfP6PB9Hw+im89l4PAoHwBlstOJgfmZGYmDnoGXXB4wvAaAjeEY+nINuslVK1D42jb8wNj195vdhhkEh5fnjPQeugE/1jbpiNkq4L9GBZUTA4aB8ahy8gI8tsjHmO0L+7aEoe9/i1f98lFYnLioDYi9AGHR7tvVapWQoAuHixcuG+4/RA2G6HaH6/qwVfeeowPvLznRhxxm9E77W7cKp3DJIEXBTSW3Ll8goAwKvHeiN+N4iIaHZicEA0BcrzbGF7AG65oBqAUgojJgHtahqExWTAwx9bp9W4b1hQgrI8K0bGvdh+qg8ur19rGL5UvXCMZmLPgcvrx7f/2ohdTYN4cn87vv/icfzTo3u1EidAuRvfPjQOgwSsmTABCVAacwGga8SFQYdHKymqKsyC2ajvfzpC+w5EOdCcfFtECVMsFWpDcq+69OztU8rd7/NqipBtMSV8fXWUsiLRb7CgNCfmroUlc3JhMkgYdnrROaJ89um+McgyUJRtjrtfIVSsXQcia7CwLEdrmgaANdUFyLOaMOz0RmQtQsmyjN/sVCZgdQyP48tPHoo7llRkDVZWFqAgO/h5GxYWI8diRO+oO6KEioiIZicGB0RTZGVlcDfCprrghf1HN8wDABgk4P4Pn4cNC4N3co0GCe9fpUxE+suBTuxuGoTbF8DcAlvcO+W1Wn3/OAIBGdtO9sPh8aM8z4rPX70EFy5QyoaeP9KtvUZkDZbNyUeuNfJCO89mxny1fOho54hWvqKnpEjQJhYNOoP9BjpLioBgWVH/mAdefwBvn1ZKrDbWlcR7mUb0JYROKxKTihbEmThkNRm1f++j6kXzqZBm5EQ7HoRYwYFodF5bHR6UmYwGXKT+3bbFmVq0t2UIJ3rGYDUZYDZKeOFoN363K/YUrB3qv9umCf9uVpNR22nx6jGWFhEREYMDoimzWa3tvn1DLYwhd6ivWl6Or75/OX7+sXW4buWciNfduKYSAPByYw9ealQu5i9ZXBr3gnRuQRZMBgkefwA9oy48f0Tdprx6Lv71ysX49gdXAlDKmZweZea/CA5iNTkDwIqQhW4tYlKRjmZkQcscDI0nPakIAIqyLTAblb93j92FneodcPFvm4i4OO8bdWvjRE/3KX+Puhj9BsLEsqqTajPyIh3NyEKwrGhC5kBdsLa2NjJjc4maIYo30vR3atbgg2ur8OXrlgEAvvXXRhzrskd9vsgcRAuqrlymlBa9rI7LJSKi2Y3BAdEU+cdN8/H01s347OWLwh6XJAmfuGShVu890fm1hagqzILD48cfdrcBiN9vACgZB3FH/nSvQ5uGtEXNQiwuz0VtcTY8voB2R1pXcKBmP450jGhlRfN1jDEVQsudtO3IOicVAYDBIGm7Drad7MeAw4MsszFiEVwshdlmZE8YJ9rUr5YVJdhVEBxHqwYHPcrrluhsRgaCi9C6hl1aTb8sy1GbkYWL1cBnX8tQ1BGjgw4P/nZYCRo/elEt/vniBbhiWTk8vgC+8uShiOeLrI3JIGkZpFCXLyuHQQKOddkjghgiIpp9GBwQTRGT0YC1NYUx69pjkSQJN6xRLup9ARmSFLxgjEfc0X9sTytGXT6U51lxQW2R9p5XqcHIK409cHn9Wk17/OBAuXve2GnXGmhrJ1FW1DrJsiIAKFdLi/68X5ngtH5BMSwmff/TJUlSsO9AvfA9o2YOFpbGv8gXwUFj54SyIp3NyIAyitUgAR5/AP0Opam6bXAcQ04vLEYDls2NfK8FpTmoLLDB4w9gT/NgxPf/tLcNHn8Aq6sLsLq6EJIk4bu3rIIkKeNRe+3hzc+ipOi82sKofRrFORbtd+A1lhYREc16DA6IMtCNqyu1r1dXFaBIRwOsuEsvlqhdt3JOWGAixla+9l4vDrQNw+uXUZZnjVvmIy6QmwYc2sVxUj0HRcFeiGBZkf7XA8Gm5N3qhfJmnf0GQujEoj3Ng+gdVS7S5ycoK6pX/+6dIy702F1oHlCCisVJZA7MRoM2EUlkTg6oJUXLK/NhNUWOppUkSes72NU0EPa9QEDG79UN2x/dUKs9Xp5nQ73a1P7OmfDXBEuKYgeYIov1CkuLiIhmPQYHRBloRWW+tr03UUmRIDIHYiLl9Svnhn1//YJi5NlMGHB48IvtTQCAdfOK4vYylOZaMSffBlkOjmVNpudABAJjbp/WCKx3AZogmpIFvf0GgshUvNzYg4//cg8AZbRs6JSgaPJsZi0QevZgJwIykG8zhU2h0mPiIrSDWjNyQczXXKQ2qe88E545ePt0P1oGnMizmrTeFEE0G4cu0PP5g2VkE5uRQ4kJWnuaByO2d09GvMlJRESU2RgcEGUgSZLwnzfU47KlZfg/G+fpek1NyB35khxLRH252WjA5UuV7IHoSYhXUiSI7AEAlOVZdY0QFbIsRpTmKhfTYm7/3EJ9Ow6E8pBdBAVZZm3sq14iQHntvV6MuX3YuLAEP/nwWl2vFX/3p9WldIsr9E8qEkRw0NillCeJSUXRxscKG9Xg4GDbsNZADgRLq24+vyri5yAmYoVmDnY3D2LQ4UFRthnr4vysl1bkoSjbDKfHj0NqZmOyjneP4rz/ehl3P34AvhQEGqFaBhxh27KJiCj1GBwQZajLl5Xj0Y9fiAqdC8NC7+hfu3JO2IQk4ar68Cbo8/UEB1XBO9zzksgaCKLvAFCyANFKaeIJ/ftvXFgS9e8VT2im4vzaQjx8x7qYm6YnEj0XRzqUpuQlSUwqEkQQ0PD6adz71CEcUUejxmuqri7KQlVhFnwBWWsc9/gCeFntCZiYNQCUzJDRIKFlILhT4kV1dO3V9RVxd0sYDJI2yWjHqYGI7/sDMt5tHcJ/v3oSP3zpONy+yEZp4dvPNWLY6cWf3+3Al544lLLlavtbh3D1j97Clp9uQ59aGkZERKnH4IBohggNDrZMKCkS3rekDCb14tpiMoRlBWIJfU4yzchCaEYj2ZIiILysaPOi5PoNAKUR12pSmsMf/acLkRNlp0Ms9RP+fRaV629GFv7PRfNw56ULAQCP7W6D2xdAvs0Ud+qTJEnYsFDJ/OxUMwFvn+7HqMuHspBG81C5VhNWq6VK75weQCAg44WjSnAQbWTuRCJbMbFn4b9fPYnzvvUSbn5wB3748gn892uncP+rJ6O+x5sn+rDtZD/MRglGg4Sn3u3A1/5y5KzLjAbG3Nj6u/3w+AMYcHjw1acPs3SJiGiKMDggmiEKss245fxqXLW8HBctjBxZCShlOaLcaHVVga67+KHBwbxi/WNMhdCgpSrJZmRgQuYgTlNtLNVF2dj71avw1Gc2Id8Wv89goonBUzLNyILFZMC/b1mO339ig9acfF5tUcIpVhP7Dl5Qx5deu6Ii5mtDL/APtA+jx+5GrtWkq09DZA72tQxpmYH3uu344csnYHf5kG8zaVOzfvbmmYgNzv6AjPv+dgwA8LGN8/Gjv18DSQJ+u7MV33y2cdIlRv6AjH97/AC6RlyoLlL2ebx4tAd/Odg5qfcjIqL4GBwQzSA//Ps1ePiO9XFLSG5bXwMguAMhkarCLK15N5lJRUJoWVEyC9CEeSXZWFqRh4sWFqMuwW6CWPJs5qRHygLKFKDQBuTFkygrEjYtKsUL/3YJ/mPLcnz9xvqEzw/tO7C7vNpCvFhZISCk7+D0AF5QS4quWFauKwisK8tFWZ4Vbl8A77YqfbifZpIAACAASURBVAePqVuXr1pegXe/dg1++4kN2LJqDvwBGV9+8lDYBf9T+9vxXvco8m0m/OsVi/CBtVW47+ZVAIBHdzTj9p/vQtdI8nsU7n/1JLad7EeW2Yhf3LEed125GADwtWeORoxtJaLpyR+QtUWVlH768+tENCN8YG0VNi8qRXF24vGogFLicvN5VfjLwU6t1CUZZ1tWZDUZ8eLdl0KW5aSbgVOhfm4+3hztQ57VpN35n6zCbAs+qZYYJSL6DjqGx/HQG6cx5PSiKNscdZGZcMG8IliMBnSNuPAHdeSpnpIiQPk5b1xYgr8c7MSO0wNYU12Ip95VGqA/tnGe1uvxjZtW4O1TAzjSYcfD25vwqUsXotvuwo9ePgEA2Hr5IhSqv1sfvrAWOVYT7n3qMHY3D2LLT7fh7quXhE2KkiQJEpR9CxsXloQFcW+f6sf9ryklTP/35pVYOicPC8ty8FJjN4502HHvU4fx8B3rYv5e+AMyDneMoH5uvu7dGPEEAnLcIHPH6X58/8Xj6LW7ce+WZXj/qrlp+Z0lmm7ueuxdvHmiD0/9yyYsSWKXDE0NBgdEs5CYIKTXN25aga/dUD+pu+81YWVFyQcHQrouslZU5uPNE31YVJF7Ts8g+g6e2t+BX2xTRs9eUz8nblYoy2LE2tpC7G4ahN3lg9VkwGVL9Y3CBZTSor8c7MTO0wOoKcrCqMuHmuKssCV85Xk2/OcN9fjCnw7ihy8dR8PrpzDqUiYqVRVm4Y5N88Pe88Y1lVhVVYDPPrYfRzrs+NozR2N+/q0XVOP7t66GJEkYdHhw9+MHIMvARy6swd+dXw1Ambr1ww+txQ3/vQ2vvteLF4/2RA2A3m0dwn8+cwRHOuy4ZHEpHv34hVGb2X3+AJr6HbCajDF7ajy+AB547SR+vq0Jn7xkAe65ZmnY9493j+I7fzuGN0/0aY999vfv4sml7fjWB1aG/XdAGPf4YTMbGDzQrHekYwTPqft57n/1JB64/fw0n2jyxj1+/MMvdiHfZsLDd6xPeoBGpmBZERHpMpnAAADmFti0JuiaswgO0uXGNZUoyjbjg2urzvlni74Dj1q+c92qxFmA0H0G71tSltToWfHad9uG8OiOZgDAh9fXRvzsbzm/CpcuKYPXL2PU5YNBUvoxfnzb2qiToOaX5uDJz2zCXVcuxsWLSrF5UQk2LyrBproSbFxYgosWKpOWntjXjh+/chKyLONLTxxC76gbi8pz8bUbVoS939I5efjUpXUAgP/7t8awcoQRpxdffuIQbn5whzZlatvJfvz0lRPac1xeP37w4nHc9MB2rPj6i7j6x2/hyh+9gb1RNlKf6BnF3z30Nu5/7RTGvX7c/9opvHE8uCxuf+sQbnpgO9480QeTQcIdG+fhrisWwWI04PXjfbjmx29hX0v4+754tBurv/kirvvJNvz53faUj3wlmk4e3nZG+/q5w1040zeWxtOcnd/ubMG+liG8frwPT+xrS/dxJk2SZ/HIB7vdjoKCAoyMjCA/P7nZ6USk3/+8eRptQ0781wdW8k5pEtoGnbjke68DAPJsJuz76tUJy2N2nRnAbf+7EwDw49vW4ObzqnV/nizL2Pzd19A5otTymwwSdtx7BcrzIsupHG4fdp4ZQFVRFhaU5iQ9onaix3a34t6nDgNQehxeOdYDi9GAp7dujpgaBQBOjw9X/OBNdNtd+MI1S/DZKxZj2OnB7T/fhcYuJSi49YJqrKzMxzeebQQA/PIf12NxRS4+89v9ONwRbKg2GiT4AzLmFtjwt7su0TaS/3FvG7769BF4fAEUZpuxproQb57oQ2muFS/82yVwuv24+cG3MeDwYOPCEtz3d6u0zdunesfwlScPYW/LEKoKs/DcXRejMNuCzuFxXPeTt2B3BfdXVBdl4YvXLsUH0hCAUtDT73agY3gcd166EOY4GTpKnc7hcVzyvdfhD8hYWpGH4z2j+Pt11fjerWvSfbSkOdw+XPq91zHg8ABQ9gK98YXLkpqQl2qTvc5lWRERTblPva8u3UeYlkL7Dq5aXqGrbn5tbSEq8q3w+AK4YllFwueHkiQJG+tK8eT+dgDKfoRogQEA5FhNuHJ5cu8fz0curEXX8Djuf+0UXlH3OXzl+mVRAwMAyLaYcO+WZfjcHw6g4fXTuHbFHHzhTwfR2GVHaa4VP/uH87FuvtKfcabfgV+/04J/e/wAJAkYVvs3/uP99Vg/vwhFORZ84IG30dTvwBf+dBA//9g6PPjGKfzgJSXbcPnSMvy/W1YjP8uMmx7YjhM9Y7jnjwfRPuTEgMODFZX5ePiOdWEXAYvKc/HoP12IG+7fhuYBJ7785CE8+NELcPfjB2B3+bCmugDXrJiDR7Y3oX1oHJ/7wwE0dtnx5WuXwWCQMOb24RfbmtA+5MSW1XNx6eIyGA0SZFnG0U47tp/qx5m+MTT3O9Ftd+Hq+gp88dqlYZkbjy+AkXEvsi1GZJmNk87+zQYNr5/C9188DkApc7n/I+cxQDgHfvl2E/wBGZvqSvD5a5bilod24Kn9HfjcVUsm1aOWTr9+pwUDDg9qi7MhSUDLgBP/+9YZ3H31knQfLWnMHDBzQEQZ7AcvHsfP3jyNx+68COvn62sI77W7EJCBOQXJN1A/sa8dX/jTQQDAr//pQly6RH/PwtmSZRlffOIQntjXjsuXluGRf1wfN9MkyzI+9LN3sLdlCBaTAR5fAEXZZvzhzo1YOifY1Oj2+fH3/7MTB9Xt1KurC/DQP1wQdvFxtHMENz+4Ax5fAGtqCrXn/stldfjitUu1cxzrsuMDDW/D41NKgSoLbPjz1s0xlxUebh/B3z30Nrx+GRcuKMbupkFkW4z4212XYH5pDlxeP/77tZNoeP00ACUgu3RJGX76ygn0j3m096kqzMKmuhLsOD2AjuHoU58WlefiJ7etRUmuBY/uaMZju1rDMhR5VhMqC7NQWWhDQZYZPXY3OkfGMTjmwcKyHKypKcTq6kKU5FhgUndVDDo8aBscR/uQE2ajsi/k/NoizCmwoX3IieYBB3rtbljNBmSZjci1mrFkTm7MoDLUiNOLF4524WD7CJxuH5wepTxs86JSXLdyju4FkPF4/QE8vK0Jj+1uRWWhDZctLcdlS8uwNGTbeWhgILJI19RX4IHbz48ZkMuyjANtw3jrRD/mlWTj/avnZkww4fMHsO1kP4wGCevmFyVVWngu2V1ebLrvNYy5ffjlx9fj8qXl+Mj/7sQ7ZwZwx8Z5+OYHVup+r/YhJ073OeAPBOAPAKW5FqytKTxnmepRlxeXfO91DDu9+OGH1iDLYsS//G4/ssxGvPHFy1LyuzwZk73OZXDA4ICIMlggIMPtCyDLcnZlO3r1jrpw5Q/eRE1xNv76rxef87vNgYCMQx0jWFGZr+ti60jHCG58YDtkGci3mfD7T16ElSFbvYXO4XF84U8HsWxOPr503dKovRG/3dmCrz59BAAgScDXbqjHxzcviHjeI9ub8K2/NiLXasITn9mIZXPi//+Ph7edwbefO6b9+Xu3rsbfr6sJe87T73bgS08e0oIOAFhYmoNNi0rw7MEujIx7tcdtZgMuXlSGlVX5WKCWMX37uWPoG3Vr/T2+FG2mnqyqwiysrS1E/dx8LC7PxeKKPARkGe1D42gbdOKtE31443if1k8Tzfm1SrCysCwHtcXZ6B/z4ETPKI53jyIgyyjLtaI0z4ra4mxsqivBgtKcsIvBvc2D+Pc/H8aJnsga9jybCcvn5KMox4wXjyqZqi9euxT1lfn41G/2weML4KrlFfjhh9agIDs4XavX7sIvdzTj2YOdaB8KBmnVRVn41PvqcE19BfwBGT6/DG8goPxffwAmo4R5xTlx/3vs8vr/f3t3HhXVffYB/HtnmBmGZRj2gbAIbmgECy6UaKypRuS11SgusfSolZjGamKW5lhzjhq1rVbf6mmWWk9fFfPG16hpXGrSVlyjghuKa0QhCBpAFBgYlmGGmd/7BzB1AgKOCQPl+zlnzoF7f3fmuQ/PzNyHu+FelREllUaUVBmhkMvQN8AD4b7uMFusOJX7AEdz7iPvfjX8PVUI9nLFU1o1BgZ74elgDdQKOT6/UowNh27i6/s1AACFXEJsmDfiI3wQE6LF4BAvqJVyZN/RI6ugAg+q6/HTmGAMj/Cx5e6+oR4ZeQ8wIEjT5pWD6hssKCirxcXCCmTf0SO3tBpmi4C16cpyTwdrEB/hg/gIX7gqZNDXmqGvM8MqBFQuMvzjSgk+OJqLvgEeOPjGKEiShFO5D5DyP2egcpHhrXGNVzZzV7mgtt4CfZ0JBmMDvN2UiGiqiexCPXZn3bHdD+ZhU4eEYNWkQbacG4xmZOaVoXeAB3r7//uy1FfuVuJvF+5CLpPwX9FBiAtrvakwW6yorbfAXSVvcWGID47cwn8fvIlIP3ccfGMU5DIJU/+SiayCCkwbEoJ105xzmBSbAwewOSAiaqm8xgSliwweTjxW9nF8eDQXf79UhDXJMfhBqNbh5xFC4J09V3HgchF+NzkaEwcHP3Jc+vV7LTYy2nre1G3nceRGKSZEB+GDn8W2uvGRVVCBVz7Ogtlixetj+iLlh+FQyGUwmi34/HIxbpRUYXiEL0b28WuxkVleY8I7n12x3RU7PsIHLz0bief6+8NksaLOZEFFrRlF+joU6eugrzMjUKNCsJcaWjclcu4ZcOmOHle/qUSNqQENFoEGq4CXWoFQbzVCfdxQU2/BhcIKXCuqhNkioFbIEe7rhmCtunHDyWRBRa0J+Q9q0NEtiyidJ8YMCIC3mxJqpRwGYwMOXivBhaZ7bTyOYC9XRAVpUFZdj+JKI0oN9QAaL5P763H9YWqw4NjN+8jMK0N9g31T8nZifyx4rg+Axjt9z/voPExNdzOfP7oPkuOeQlrGbWw5lQ+juXFZN6UcI/v44UJhhd1enkeRpMamqZevOxTyxr+/RQAPDPUoqTKivKb153CRSZAkwGx5dFJlUuN6NsehdVPAXenyyL1M3xYT4oXJsU8hI68MR26UwmIVkKTG++G8PqYvNGoF0q/fw+Gv7iH3fjUqasyorm9o/4k74OFmWQiByX/OQPadx/v7SxLQL8ATqqYrgF25q4dVNNbX6inROHqjFGkZt2170voEeGB0P3+cK6iw7SVs9pRWjdgwLaqMDdDXmlBRa4K+xgzDQ+vr6erSWLMKOVQKGXJLq1FrsuBPL/7Adu7QhcIKTPlzBiQJ+PzVZx95iOT3ic2BA9gcEBHRt1ms4ju/BGGdyYIjN0oxZkBAq3stmhnNFsgkyaH7MgghcCq3DN7uCjwd3HLvyXfFaLagymiGv4eq1SbHYDTjyt1KZN/V42aJAbdKq5FbWg25TEKotxtCvNUYEKTBTwYHPXKvS0mlEV/ebPwved79GhSW18DbTYkonSf66zRQucjwoLoepYZ6XCuqxIUCfYu9EJIEzBgait8kRdnuvQE0nouRd78aXxVXIafEgH6BnkgeYn/i/tn8cizdexU59wwtYosL02LuyAiMiQqEWilHncmCXefv4K8nvsbdijoo5BJcZDK4yCUo5DK4yKSmnLW/Me2qkCHIS41AjQpGsxW5pdW2jfAwHzeM7u+PH4RqUV5jQnGlEQVltbhWVIniposIeKpc8NKzkZg7shc8VC4oKKvFqbwHuFiox5W7lbhVaoBVNO7pGBLuDZWLDPuyi1o0S5F+7vj6QY0tj4/aUnRTyhET4oUfhHpjYNPeC7kMMJqtyCqowOmvy3C9uApCAO5KObzUCsjlEurNVtQ3WBGl88RHqcPtLmiQd78a/5tZAH2tCVXGBlTXN8BdKYfWTQkPlQvuG+qR/6AGt8tqEOTliuS4EEwZEmJ3mGBG3gO8tuNii6YtyMsVD6rr7RothVxC0qAgyGUSDl4rQY3JsZuxRek88flrz9p9diz8vwuorDPj3YlPd+gfCd81NgcOYHNARET0/Wve1Pi+jgGvM1lw7nY5CstrEahxRVDTITfNV55yhMUqsC/7G/zx4E18o69Dv0APvJ0YhbEDAlpdj7bWUQiB8hoT8u7X4E55LawPjfV1V0Ln1Rizl1pht7wQAsWVRlisAiHe6kfmr9RgRF5pDQYGaewOg/q2WlMD6kwW+D50r5uy6np8fLoQJ27dR2yYFtOGhqJfoCeuF1XhT4dv2g67ig3T4vmBgRjeywe+Hir4uCmhUbu0+zetM1kglznW8LalvRtj3qsy4tX/u4izt8sx6CkNFj7XB+MG6mCob8DRG6U4lfsAvfzcMWNYqO3eP3UmC47llOIbfR281Ap4uynh7a6A1k0Jbzcl3FWNe7f0tWZU1plgNFtR32CBqcGKIeE+8Pe0v4eQ0Wxp858B3zc2Bw5gc0BERERtqW+wIKfEgKeDvbrtTa2eRHFlHVxkshYbvt2B1Spwp6K26QpCPe9vx0uZEhEREX3HVC5yxIQ4fi5Ldxfk1b0uKfowmUxCuK+7s8PodrrGdbeIiIiIiMjp2BwQEREREREANgdERERERNSEzQEREREREQFgc0BERERERE3YHBAREREREQA2B0RERERE1KRH3+eg+f5vVVVVTo6EiIiIiOi707x9+7j3O+7RzYHBYAAAhIaGOjkSIiIiIqLvnsFggJeXV4fHS+Jx24n/IFarFUVFRfD09HTKbbWrqqoQGhqKO3fuPNZtrYm5e1LMn+OYO8cxd45j7p4M8+c45s5xzs6dEAIGgwHBwcGQyTp+JkGP3nMgk8kQEhLi7DCg0Wj4hnMQc/dkmD/HMXeOY+4cx9w9GebPccyd45yZu8fZY9CMJyQTEREREREANgdERERERNRE/u67777r7CB6MrlcjtGjR8PFpUcf4eUQ5u7JMH+OY+4cx9w5jrl7Msyf45g7x3XH3PXoE5KJiIiIiOjfeFgREREREREBYHNARERERERN2BwQEREREREANgdERERERNSEzYETffjhh+jVqxdcXV0RHx+Ps2fPOjukLmf16tUYNmwYPD09ERAQgBdeeAE5OTl2Y0aPHg1Jkuwer7zyipMi7jrefffdFnmJioqyzTcajViwYAF8fX3h4eGB5ORk3Lt3z4kRdx29evVqkTtJkrBgwQIArLmHffnll/jpT3+K4OBgSJKEvXv32s0XQmDZsmUICgqCWq3G2LFjcevWLbsx5eXlSElJgUajgVarRWpqKqqrqztzNZymrfyZzWYsXrwY0dHRcHd3R3BwMGbNmoWioiK752itXtesWdPZq9Lp2qu9OXPmtMjL+PHj7cb01NprL3etff5JkoR169bZxvTUuuvIdklHvl8LCwsxYcIEuLm5ISAgAG+//TYaGho6c1Ueic2Bk+zcuRNvvvkmli9fjgsXLmDw4MFITExEaWmps0PrUo4fP44FCxbg9OnTSE9Ph9lsxrhx41BTU2M3bt68eSguLrY91q5d66SIu5ann37aLi8nT560zXvjjTfw97//Hbt378bx48dRVFSEKVOmODHaruPcuXN2eUtPTwcATJs2zTaGNdeopqYGgwcPxocfftjq/LVr1+K9997DX/7yF5w5cwbu7u5ITEyE0Wi0jUlJScG1a9eQnp6OAwcO4Msvv8TLL7/cWavgVG3lr7a2FhcuXMDSpUtx4cIFfPbZZ8jJycHEiRNbjF25cqVdPb766qudEb5TtVd7ADB+/Hi7vOzYscNufk+tvfZy93DOiouLsWXLFkiShOTkZLtxPbHuOrJd0t73q8ViwYQJE2AymZCRkYFt27YhLS0Ny5Ytc8YqtSTIKYYPHy4WLFhg+91isYjg4GCxevVqJ0bV9ZWWlgoA4vjx47ZpP/rRj8SiRYucGFXXtHz5cjF48OBW5+n1eqFQKMTu3btt07766isBQGRmZnZWiN3GokWLRO/evYXVahVCsOYeBYDYs2eP7Xer1Sp0Op1Yt26dbZperxcqlUrs2LFDCCHE9evXBQBx7tw525h//OMfQpIk8c0333Re8F3At/PXmrNnzwoAoqCgwDYtPDxcbNiw4fsOr0trLXezZ88WkyZNeuQyrL1GHam7SZMmiR//+Md201h3jb69XdKR79cvvvhCyGQyUVJSYhuzceNGodFoRH19feeuQCu458AJTCYTsrKyMHbsWNs0mUyGsWPHIjMz04mRdX2VlZUAAB8fH7vp27dvh5+fHwYNGoQlS5agtrbWGeF1Obdu3UJwcDAiIyORkpKCwsJCAEBWVhbMZrNdDUZFRSEsLIw1+C0mkwkff/wx5s6dC0mSbNNZc+3Lz89HSUmJXZ15eXkhPj7eVmeZmZnQarUYOnSobczYsWMhk8lw5syZTo+5q6usrIQkSdBqtXbT16xZA19fX8TGxmLdunVd5vAEZzt27BgCAgLQv39/zJ8/H2VlZbZ5rL2OuXfvHj7//HOkpqa2mMe6a7ld0pHv18zMTERHRyMwMNA2JjExEVVVVbh27VonRt+67nO7tv8gDx48gMVisSsKAAgMDMSNGzecFFXXZ7Va8frrr2PEiBEYNGiQbfrPfvYzhIeHIzg4GJcvX8bixYuRk5ODzz77zInROl98fDzS0tLQv39/FBcXY8WKFXj22Wdx9epVlJSUQKlUttjACAwMRElJiZMi7pr27t0LvV6POXPm2Kax5jqmuZZa+6xrnldSUoKAgAC7+S4uLvDx8WEtfovRaMTixYsxc+ZMaDQa2/TXXnsNcXFx8PHxQUZGBpYsWYLi4mKsX7/eidE63/jx4zFlyhREREQgLy8P77zzDpKSkpCZmQm5XM7a66Bt27bB09OzxWGnrLvWt0s68v1aUlLS6udi8zxnY3NA3caCBQtw9epVu+PmAdgdHxodHY2goCCMGTMGeXl56N27d2eH2WUkJSXZfo6JiUF8fDzCw8Oxa9cuqNVqJ0bWvWzevBlJSUkIDg62TWPNUWczm82YPn06hBDYuHGj3bw333zT9nNMTAyUSiV++ctfYvXq1VCpVJ0dapfx4osv2n6Ojo5GTEwMevfujWPHjmHMmDFOjKx72bJlC1JSUuDq6mo3nXX36O2S7o6HFTmBn58f5HJ5izPX7927B51O56SouraFCxfiwIEDOHr0KEJCQtocGx8fDwDIzc3tjNC6Da1Wi379+iE3Nxc6nQ4mkwl6vd5uDGvQXkFBAQ4dOoSXXnqpzXGsudY111Jbn3U6na7FhRgaGhpQXl7OWmzS3BgUFBQgPT3dbq9Ba+Lj49HQ0IDbt293ToDdRGRkJPz8/GzvU9Ze+06cOIGcnJx2PwOBnld3j9ou6cj3q06na/VzsXmes7E5cAKlUokhQ4bg8OHDtmlWqxWHDx9GQkKCEyPreoQQWLhwIfbs2YMjR44gIiKi3WWys7MBAEFBQd93eN1KdXU18vLyEBQUhCFDhkChUNjVYE5ODgoLC1mDD9m6dSsCAgIwYcKENsex5loXEREBnU5nV2dVVVU4c+aMrc4SEhKg1+uRlZVlG3PkyBFYrVZb09WTNTcGt27dwqFDh+Dr69vuMtnZ2ZDJZC0Omenp7t69i7KyMtv7lLXXvs2bN2PIkCEYPHhwu2N7St21t13Ske/XhIQEXLlyxa45bW78Bw4c2Dkr0hYnnxDdY33yySdCpVKJtLQ0cf36dfHyyy8LrVZrd+Y6CTF//nzh5eUljh07JoqLi22P2tpaIYQQubm5YuXKleL8+fMiPz9f7Nu3T0RGRopRo0Y5OXLne+utt8SxY8dEfn6+OHXqlBg7dqzw8/MTpaWlQgghXnnlFREWFiaOHDkizp8/LxISEkRCQoKTo+46LBaLCAsLE4sXL7abzpqzZzAYxMWLF8XFixcFALF+/Xpx8eJF29V01qxZI7Rardi3b5+4fPmymDRpkoiIiBB1dXW25xg/fryIjY0VZ86cESdPnhR9+/YVM2fOdNYqdaq28mcymcTEiRNFSEiIyM7OtvsMbL6iSUZGhtiwYYPIzs4WeXl54uOPPxb+/v5i1qxZTl6z719buTMYDOLXv/61yMzMFPn5+eLQoUMiLi5O9O3bVxiNRttz9NTaa+99K4QQlZWVws3NTWzcuLHF8j257trbLhGi/e/XhoYGMWjQIDFu3DiRnZ0t/vnPfwp/f3+xZMkSZ6xSC2wOnOj9998XYWFhQqlUiuHDh4vTp087O6QuB0Crj61btwohhCgsLBSjRo0SPj4+QqVSiT59+oi3335bVFZWOjfwLmDGjBkiKChIKJVK8dRTT4kZM2aI3Nxc2/y6ujrxq1/9Snh7ews3NzcxefJkUVxc7MSIu5Z//etfAoDIycmxm86as3f06NFW36OzZ88WQjReznTp0qUiMDBQqFQqMWbMmBY5LSsrEzNnzhQeHh5Co9GIX/ziF8JgMDhhbTpfW/nLz89/5Gfg0aNHhRBCZGVlifj4eOHl5SVcXV3FgAEDxO9//3u7DeD/VG3lrra2VowbN074+/sLhUIhwsPDxbx581r8A66n1l5771shhNi0aZNQq9VCr9e3WL4n11172yVCdOz79fbt2yIpKUmo1Wrh5+cn3nrrLWE2mzt5bVonCSHE97RTgoiIiIiIuhGec0BERERERADYHBARERERURM2B0REREREBIDNARERERERNWFzQEREREREANgcEBERERFREzYHREREREQEgM0BERERERE1YXNAREREREQA2BwQEfV49+/fx/z58xEWFgaVSgWdTofExEScOnUKJpMJfn5+WLNmTavLrlq1CoGBgTCbzUhLS4NWq3U4DkmSsHfvXoeXJyKiJ8fmgIioh0tOTsbFixexbds23Lx5E/v378fo0aNRVlYGpVKJn//859i6dWuL5YQQSEtLw6xZs6BQKJwQORERfdfYHBAR9WB6vR4nTpzAH/7wBzz33HMIDw/H8OHDsWTJEkycOBEAkJqaips3b+LkyZN2yx4/fhxff/01UlNTO/RagBuO6gAABHpJREFUJpMJCxcuRFBQEFxdXREeHo7Vq1cDAHr16gUAmDx5MiRJsv0OAPv27UNcXBxcXV0RGRmJFStWoKGhwTZfkiRs3LgRSUlJUKvViIyMxKeffvoEWSEi6rnYHBAR9WAeHh7w8PDA3r17UV9f3+qY6OhoDBs2DFu2bLGbvnXrVjzzzDOIiorq0Gu999572L9/P3bt2oWcnBxs377d1gScO3fO9pzFxcW230+cOIFZs2Zh0aJFuH79OjZt2oS0tDT87ne/s3vupUuXIjk5GZcuXUJKSgpefPFFfPXVV4+TCiIiApsDIqIezcXFBWlpadi2bRu0Wi1GjBiBd955B5cvX7Ybl5qait27d6O6uhoAYDAY8Omnn2Lu3Lkdfq3CwkL07dsXI0eORHh4OEaOHImZM2cCAPz9/QEAWq0WOp3O9vuKFSvwm9/8BrNnz0ZkZCSef/55rFq1Cps2bbJ77mnTpuGll15Cv379sGrVKgwdOhTvv/++w3khIuqp2BwQEfVwycnJKCoqwv79+zF+/HgcO3YMcXFxSEtLs42ZOXMmLBYLdu3aBQDYuXMnZDIZZsyY0eHXmTNnDrKzs9G/f3+89tprOHjwYLvLXLp0CStXrrTt4fDw8MC8efNQXFyM2tpa27iEhAS75RISErjngIjIAWwOiIgIrq6ueP7557F06VJkZGRgzpw5WL58uW2+RqPB1KlTbScmb926FdOnT4eHh0eHXyMuLg75+flYtWoV6urqMH36dEydOrXNZaqrq7FixQpkZ2fbHleuXMGtW7fg6urq2MoSEdEjsTkgIqIWBg4ciJqaGrtpqampOHnyJA4cOICMjIwOn4j8MI1GgxkzZuCvf/0rdu7cib/97W8oLy8HACgUClgsFrvxcXFxyMnJQZ8+fVo8ZLJ/f4WdPn3abrnTp09jwIABjx0fEVFP5+LsAIiIyHnKysowbdo0zJ07FzExMfD09MT58+exdu1aTJo0yW7sqFGj0KdPH8yaNQtRUVF45plnHuu11q9fj6CgIMTGxkImk2H37t3Q6XS2eyP06tULhw8fxogRI6BSqeDt7Y1ly5bhJz/5CcLCwjB16lTIZDJcunQJV69exW9/+1vbc+/evRtDhw7FyJEjsX37dpw9exabN29+8gQREfUw3HNARNSDeXh4ID4+Hhs2bMCoUaMwaNAgLF26FPPmzcMHH3xgN1aSJMydOxcVFRWPdSJyM09PT6xduxZDhw7FsGHDcPv2bXzxxRe2PQB//OMfkZ6ejtDQUMTGxgIAEhMTceDAARw8eBDDhg3DD3/4Q2zYsAHh4eF2z71ixQp88skniImJwUcffYQdO3Zg4MCBDmaFiKjnkoQQwtlBEBEROUqSJOzZswcvvPCCs0MhIur2uOeAiIiIiIgAsDkgIiIiIqImPCGZiIi6NR4dS0T03eGeAyIiIiIiAsDmgIiIiIiImrA5ICIiIiIiAGwOiIiIiIioCZsDIiIiIiICwOaAiIiIiIiasDkgIiIiIiIAbA6IiIiIiKjJ/wNHsBxsUnVvTwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "pyro.clear_param_store()\n",
    "pyro.set_rng_seed(1234567890)\n",
    "num_steps = 1 if smoke_test else 201\n",
    "optim = ClippedAdam({\"lr\": 0.1, \"lrd\": 0.1 ** (1 / num_steps)})\n",
    "svi = SVI(model, lambda: None, optim, EnergyDistance())\n",
    "losses = []\n",
    "for step in range(num_steps):\n",
    "    loss = svi.step()\n",
    "    losses.append(loss)\n",
    "    if step % 20 == 0:\n",
    "        print(\"step {} loss = {}\".format(step, loss))\n",
    "\n",
    "print(\"-\" * 20)\n",
    "pyplot.figure(figsize=(9, 3))\n",
    "pyplot.plot(losses)\n",
    "pyplot.yscale(\"log\")\n",
    "pyplot.ylabel(\"loss\")\n",
    "pyplot.xlabel(\"SVI step\")\n",
    "for name, value in sorted(pyro.get_param_store().items()):\n",
    "    if value.numel() == 1:\n",
    "        print(\"{} = {:0.4g}\".format(name, value.squeeze().item()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = poutine.uncondition(model)().detach()\n",
    "pyplot.figure(figsize=(9, 3))\n",
    "pyplot.hist(samples.numpy(), bins=200)\n",
    "pyplot.yscale(\"log\")\n",
    "pyplot.xlabel(\"daily log returns\")\n",
    "pyplot.ylabel(\"count\")\n",
    "pyplot.title(\"Posterior predictive distribution\");\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a poor fit, but that was to be expected since we are mixing all time steps together: we would expect this to be a scale-mixture of distributions (Normal, or Stable), but are modeling it as a single distribution (Stable in this case)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling stochastic volatility  <a class=\"anchor\" id=\"modeling\"></a>\n",
    "\n",
    "We'll next fit a stochastic volatility model.\n",
    "Let's begin with a constant volatility model where log price $p$ follows Brownian motion\n",
    "\n",
    "$$\n",
    "  \\log p_t = \\log p_{t-1} + w_t \\sqrt h\n",
    "$$\n",
    "\n",
    "where $w_t$ is a sequence of standard white noise. We can rewrite this model in terms of the log returns $r_t=\\log(p_t\\,/\\,p_{t-1})$:\n",
    "\n",
    "$$\n",
    "  r_t = w_t \\sqrt h\n",
    "$$\n",
    "\n",
    "Now to account for [volatility clustering](https://en.wikipedia.org/wiki/Volatility_clustering) we can generalize to a stochastic volatility model where volatility $h$ depends on time $t$. Among the simplest such models is one where $h_t$ follows geometric Brownian motion\n",
    "\n",
    "$$\n",
    "  \\log h_t = \\log h_{t-1} + \\sigma v_t\n",
    "$$\n",
    "\n",
    "where again $v_t$ is a sequence of standard white noise. The entire model thus consists of a geometric Brownian motion $h_t$ that determines the diffusion rate of another geometric Brownian motion $p_t$:\n",
    "\n",
    "$$\n",
    "  \\log h_t = \\log h_{t-1} + \\sigma v_t \\\\\n",
    "  \\log p_t = \\log p_{t-1} + w_t \\sqrt h_t\n",
    "$$\n",
    "\n",
    "Usually $v_1$ and $w_t$ are both Gaussian. We will generalize to a Stable distribution for $w_t$, learning three parameters (stability, skew, and location), but still scaling by $\\sqrt h_t$.\n",
    "\n",
    "Our Pyro model will sample the increments $v_t$ and record the computation of $\\log h_t$ via [pyro.deterministic](http://docs.pyro.ai/en/stable/primitives.html#pyro.deterministic). Note that there are many ways of implementing this model in Pyro, and geometry can vary depending on implementation. The following version seems to have good geometry, when combined with reparameterizers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(data):\n",
    "    # Note we avoid plates because we'll later reparameterize along the time axis using\n",
    "    # DiscreteCosineReparam, breaking independence. This requires .unsqueeze()ing scalars.\n",
    "    h_0 = pyro.sample(\"h_0\", dist.Normal(0, 1)).unsqueeze(-1)\n",
    "    sigma = pyro.sample(\"sigma\", dist.LogNormal(0, 1)).unsqueeze(-1)\n",
    "    v = pyro.sample(\"v\", dist.Normal(0, 1).expand(data.shape).to_event(1))\n",
    "    log_h = pyro.deterministic(\"log_h\", h_0 + sigma * v.cumsum(dim=-1))\n",
    "    sqrt_h = log_h.mul(0.5).exp().clamp(min=1e-8, max=1e8)\n",
    "\n",
    "    # Observed log returns, assumed to be a Stable distribution scaled by sqrt(h).\n",
    "    r_loc = pyro.sample(\"r_loc\", dist.Normal(0, 1e-2)).unsqueeze(-1)\n",
    "    r_skew = pyro.sample(\"r_skew\", dist.Uniform(-1, 1)).unsqueeze(-1)\n",
    "    r_stability = pyro.sample(\"r_stability\", dist.Uniform(0, 2)).unsqueeze(-1)\n",
    "    pyro.sample(\"r\", dist.Stable(r_stability, r_skew, sqrt_h, r_loc * sqrt_h).to_event(1),\n",
    "                obs=data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use two reparameterizers: [StableReparam](http://docs.pyro.ai/en/latest/infer.reparam.html#pyro.infer.reparam.stable.StableReparam) to handle the `Stable` likelihood (since `Stable.log_prob()` is undefined), and [DiscreteCosineReparam](http://docs.pyro.ai/en/latest/infer.reparam.html#pyro.infer.reparam.discrete_cosine.DiscreteCosineReparam) to improve geometry of the latent Gaussian process for `v`. We'll then use `reparam_model` for both inference and prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "reparam_model = poutine.reparam(model, {\"v\": DiscreteCosineReparam(),\n",
    "                                        \"r\": StableReparam()})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step 0 loss = 80.7915\n",
      "step 50 loss = 2.49764\n",
      "step 100 loss = 6.18623\n",
      "step 150 loss = -1.42891\n",
      "step 200 loss = -2.48601\n",
      "step 250 loss = -2.75234\n",
      "step 300 loss = -2.80716\n",
      "step 350 loss = -2.64854\n",
      "step 400 loss = -2.93349\n",
      "step 450 loss = -2.90964\n",
      "step 500 loss = -2.93564\n",
      "step 550 loss = -2.98376\n",
      "step 600 loss = -3.01648\n",
      "step 650 loss = -3.01208\n",
      "step 700 loss = -3.04329\n",
      "step 750 loss = -3.03045\n",
      "step 800 loss = -3.04258\n",
      "step 850 loss = -3.06856\n",
      "step 900 loss = -3.05272\n",
      "step 950 loss = -3.06414\n",
      "step 1000 loss = -3.06487\n",
      "--------------------\n",
      "h_0 = 0.3713 ± 0.01079\n",
      "r_loc = 0.05134 ± 0.002976\n",
      "r_skew = 0.0001597 ± 0.0002002\n",
      "r_stability = 1.92 ± 0.001772\n",
      "sigma = 0.2373 ± 0.000313\n",
      "CPU times: user 38.1 s, sys: 6.95 s, total: 45.1 s\n",
      "Wall time: 45.1 s\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "pyro.clear_param_store()\n",
    "pyro.set_rng_seed(1234567890)\n",
    "num_steps = 1 if smoke_test else 1001\n",
    "optim = ClippedAdam({\"lr\": 0.05, \"betas\": (0.9, 0.99), \"lrd\": 0.1 ** (1 / num_steps)})\n",
    "guide = AutoDiagonalNormal(reparam_model)\n",
    "svi = SVI(reparam_model, guide, optim, Trace_ELBO())\n",
    "losses = []\n",
    "for step in range(num_steps):\n",
    "    loss = svi.step(r) / len(r)\n",
    "    losses.append(loss)\n",
    "    if step % 50 == 0:\n",
    "        median = guide.median()\n",
    "        print(\"step {} loss = {:0.6g}\".format(step, loss))\n",
    "\n",
    "print(\"-\" * 20)\n",
    "for name, (lb, ub) in sorted(guide.quantiles([0.325, 0.675]).items()):\n",
    "    if lb.numel() == 1:\n",
    "        lb = lb.squeeze().item()\n",
    "        ub = ub.squeeze().item()\n",
    "        print(\"{} = {:0.4g} ± {:0.4g}\".format(name, (lb + ub) / 2, (ub - lb) / 2))\n",
    "\n",
    "pyplot.figure(figsize=(9, 3))\n",
    "pyplot.plot(losses)\n",
    "pyplot.ylabel(\"loss\")\n",
    "pyplot.xlabel(\"SVI step\")\n",
    "pyplot.xlim(0, len(losses))\n",
    "pyplot.ylim(min(losses), 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It appears the log returns exhibit very little skew, but exhibit a stability parameter slightly but significantly less than 2. This contrasts the usual Normal model corresponding to a Stable distribution with skew=0 and stability=2. We can now visualize the estimated volatility:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = pyplot.subplots(2, figsize=(9, 5), sharex=True)\n",
    "pyplot.subplots_adjust(hspace=0)\n",
    "axes[1].plot(r, \"k\", lw=0.2)\n",
    "axes[1].set_ylabel(\"log returns\")\n",
    "axes[1].set_xlim(0, len(r))\n",
    "\n",
    "# We will pull out median log returns using the autoguide's .median() and poutines.\n",
    "with torch.no_grad():\n",
    "    pred = Predictive(reparam_model, guide=guide, num_samples=20, parallel=True)(r)\n",
    "log_h = pred[\"log_h\"]\n",
    "axes[0].plot(log_h.median(0).values, lw=1)\n",
    "axes[0].fill_between(torch.arange(len(log_h[0])),\n",
    "                     log_h.kthvalue(2, dim=0).values,\n",
    "                     log_h.kthvalue(18, dim=0).values,\n",
    "                     color='red', alpha=0.5)\n",
    "axes[0].set_ylabel(\"log volatility\")\n",
    "\n",
    "stability = pred[\"r_stability\"].median(0).values.item()\n",
    "axes[0].set_title(\"Estimated index of stability = {:0.4g}\".format(stability))\n",
    "axes[1].set_xlabel(\"trading day\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that volatility roughly follows areas of large absolute log returns. Note that the uncertainty is underestimated, since we have used an approximate `AutoDiagonalNormal` guide. For more precise uncertainty estimates, one could use [HMC](http://docs.pyro.ai/en/stable/mcmc.html#hmc) or [NUTS](http://docs.pyro.ai/en/stable/mcmc.html#nuts) inference."
   ]
  }
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